Think of a cake. When you put it in the oven, it starts off at a particular volume and then, an hour later, it has risen to perhaps double its size. It is obvious what has happened – the air bubbles that you have carefully folded into the mixture during the preparation and the little bubbles of carbon dioxide created by the baking powder have expanded as they are heated in the oven, taking the rest of the cake with it. All this time, the pressure of the air inside those bubbles has stayed the same (you know that because cakes don't usually explode when you slice them after cooking).

It is an intuitive idea that bubbles of air will expand if you heat them, as long as the pressure remains constant. It is also a fundamental component of the ideal gas laws, first written down in the early 19th century by the French natural philosopher Joseph Louis Gay-Lussac. He was working on the relationship between the volume and temperature of a gas, building on work carried out several decades earlier by the inventor and mathematician Jacques Charles who had shown that volume and temperature were proportional – heat a gas and its volume will increase and vice versa, as long as the pressure remains constant.

The first piece of the ideal gas puzzle came in the 17th century. Robert Boyle had been carrying out experiments with air, which he proposed was full of particles connected by tiny invisible springs. He found that the pressure of a gas had an inverse relationship to its volume. If the volume doubled, its pressure halved and vice versa, when the temperature is held constant.

As well as the volume/temperature relationship, Gay-Lussac extended the work and experiments, from a century earlier, of the inventor Guillaume Amontons to show that, in a fixed volume of gas, pressure was directly proportional to absolute temperature.

With the three relationships between pressure, volume and temperature measured and written down, French engineer Benoît Paul Émile Clapeyron, one of the founding fathers of thermodynamics, combined the work of Boyle, Charles and Gay‑Lussac into the combined ideal gas equation above, in 1834.

In short, the ideal gas law shows the relationship between the four properties of a gas that you need to know in order to predict how it will behave: pressure, temperature, volume and the number of particles of gas (ie atoms or molecules) present. It is "ideal" because the law is a model that assumes the particles are infinitely small points and do not interact with each other. All collisions between ideal gas particles are elastic, which means they do not lose any energy when they rebound off each other.

In practice, real gas particles do have measurable sizes and sometimes attract or repel each other. Nevertheless, the ideal gas equation is a highly successful way to understand how gases shift and change depending on their surroundings.

The law states that the product of the pressure (P) and volume (V) of a gas is directly proportional to its absolute temperature (T, measured in kelvin). On the right-hand side of the equation is the number of moles of gas present (n) in the system, where a mole is equal to 6.02214129×10^23particles, a number known as the Avogadro constant. Also on the right is the universal gas constant (R), equal to 8.3145 joules per mole kelvin.

The ideal gas equations can be used to work out how much air inside a cake will expand (though it's unlikely to be used for that) but it also applies to plenty of other situations. Ever noticed a bicycle pump get hot when you fill a tyre with air? That's because you're quickly putting energy into the air inside the pump by pushing the piston and reducing the volume at the same time, which causes the molecules to bounce around faster in a smaller volume and the gas heats up.

Refrigeration works in the opposite way to the bicycle pump. If you release a gas very quickly from high pressure (inside a storage tank, say) to a region of lower pressure (outside air at atmospheric pressure), then the gas will expand. The energy required to do this will come from the molecules of gas themselves and so the overall temperature of the gas will drop. You can see this in action when pressurised carbon dioxide inside a fire extinguisher turns instantly into a frost when it is released through the nozzle and on to a fire. More prosaically, the same mechanism keeps your food cold in a refrigerator.

The relationships between these so-called "state properties" of a gas make sense intuitively. But the ideal gas law can also be derived mathematically, from first principles, by imagining particles bouncing around a box. About two decades after Clapeyron wrote it down, August Krönig and Rudolf Clausius independently looked at the statistical distribution of speeds (and hence energy) among the particles to work out how pressure, volume and temperature related to each other in a gas – an approach known as statistical mechanics. In essence, this meant looking at the properties of huge numbers of tiny components or particles inside a system in order to calculate the macroscopic results. In other words, a box containing a gas will have trillions of particles flying around inside it in random directions, bouncing off each other and off the walls.

In this model, the kinetic energy of the particles is proportional to the temperature of the gas. Particles hitting the sides of the box translate in to the pressure of the gas.

In this "kinetic" version of the ideal gas law, the right-hand side is written slightly differently. Instead of "nR" are terms for the number of molecules in the gas and the Boltzmann constant (k) equal to 1.38065×10-23 joules per kelvin.

The two versions of the equation describe identical things. Whether it is cakes, bicycle pumps, refrigerators or even when modelling the behaviour of stars (which are, in essence, just clouds of hydrogen gas)[or planetary atmospheres including Earth], you can use these simple relations work out how what the gases are doing.

32 comments:

Errr, the 33C effect described as the "greenhouse effect" is the 33C difference between the surface temperature predicted by the bare earth model of -18C (no atmosphere or oceans) and what we measure as the near surface air Global Mean Temperature (GMT) of earth (15C) with an atmosphere and oceans.ie,http://i53.photobucket.com/albums/g43/DerekJohn_photos/David%20Archer%20Chicago%20Prof%20talks%20bollocks/Screenshot31_zpsb470da6a.png

The 33C difference you are describing here is the difference between the atmosphere's overall average temperature (-18C) and the near surface GMT temperature (15C).

Two very different comparisons indeed..... The first one, as the bare earth model is a black body model, is pseudo science. ie,http://www.globalwarmingskeptics.info/thread-2238-post-12927.html#pid12926

The second, well, if a surface is heated, then the further you go away from it the cooler it gets.ie, thermodynamics.....

Not Loschmidt, PLEASE. A rock simply can not know it's own altitude, and therefore what temperature it should be at....

The 33K greenhouse effect is the difference between the 255K [-18C] equilibrium temperature with the Sun and the 288K [15C] surface temperature.

The warming at the surface is entirely explainable by pressure, gravity, atmospheric mass rather than radiative forcing from greenhouse gases. I still call it "the 33K greenhouse effect" even though the cause is misunderstood by most.

and,"The warming at the surface is entirely explainable by pressure, gravity, atmospheric mass rather than radiative forcing from greenhouse gases."Do you not feel that sunlight IS warm?????

Please correct me if I am wrong, but you appear to be saying that gravity is a constant energy supply that warms the planets atmosphere ALL OVER, ALL OF THE TIME. Which does not agree with the daily temperature ranges we experience?

and,"I still call it "the 33K greenhouse effect" even though the cause is misunderstood by most."There is an observed 33C difference, yes, but thermodynamics is the only way within science (ie within the scientific method) that can explain it.

Yes, of course warming from the Sun is essential to bring the Earth to the average 255K equilibrium temp

Sun heats surface > hot air packets rise to upper atmosphere to release latent heat [convective cooling] > packet cools and descends and is re-compressed by gravity, which increases T at the surface [this is what I am calling the REAL greenhouse effect]. Process repeats ad-infinitum.

Yes, the thermodynamics of pressure & convection & phase change are the explanation of the 33K "greenhouse effect", not "radiative forcing"

The net heat flux from a -15C body [atmosphere] to a +15C body [Earth] cannot be +150W/m2, which is what the radiative forcing GHE requires. No such violations of any laws of thermodynamics are required for the ideal gas law explanation of the GHE.

"A rock simply can not know it's own altitude, and therefore what temperature it should be at...."

A rock, being a solid is not subject to the gas laws.

By virtue of the gas laws a gas molecules does indeed 'know' its own altitude and the temperature that it should be at because of its interaction with pressure and volume which together determine the gas density at the given height and therefore temperature.

I've produced many articles and made many blog comments on these points in recent years.

"you appear to be saying that gravity is a constant energy supply that warms the planets atmosphere ALL OVER, ALL OF THE TIME"

That is not what MS is saying.

On the day side upward convection cools the surface by taking KE away from the surface and converting it to PE higher up.

On the night side downward convection warms the surface by bringing PE back down and converting it to KE again.

On a rotating world the process is broken up into latitudinal climate zones with jet streams threading between them.

It is the length of time taken by the adiabatic process as a whole which determines the surface temperature enhancement and the adiabatic process can speed up or slow down as necessary to ensure that nothing other than more mass, more gravity or more insolation can raise surface temperature overall.

The effect of GHGs is to simply speed up the adiabatic process in an equal and opposite system response which negates the thermal effect of the GHGs at the cost of an indiscernible circulation adjustment.

Yes I do realize that and it is very unfortunate. I can't for the life of me figure out why Willis et al thinks this violates the 1st law, when in fact conventional greenhouse theory flagrantly violates both the 1st and 2nd laws. How can GHGs create 150W/m2 out of thin air, and create a net heat transfer of 150W/m2 from the -15C atmosphere to the +15C Earth. Just astonishing. How do GHGs create 584W/m2 at the base of the troposphere on Uranus from the 3.71 W/m2 received from the Sun? Just astonishing to me that physicists continue to believe this fable.

Not all, but many of the Slayers do support that there is a 33K "greenhouse effect" due entirely to atmospheric mass & gravity, not due "radiative forcing." Joe Postma & Claes Johnson included.

An isothermal profile in a gravitational field is not isentropic, for the simple reason that, firstly you are assuming all molecules have the same kinetic energy, but secondly, we know the ones at the top have more gravitational potential energy.

So, consider the following initial state ...

Molecules at top: More PE + equal KE

Molecules at bottom: Less PE + equal KE

In such a situation you have an unbalanced energy potential because the molecules at the top have more energy than those at the bottom. Hence you do not have the state of maximum entropy, because work can be done.

Let's consider an extremely simple case of two molecules (A & B) in an upper layer and two (C & D) in a lower layer. We will assume KE = 20 initially and give PE values such that the difference in PE is 4 units ...

At top: A (PE=14 + KE=20) B (PE=14 + KE=20)

At bottom: C (PE=10 + KE=20) D (PE=10 + KE=20)

Now suppose A collides with C. In free flight it loses 4 units of PE and gains 4 units of KE. When it collides with C it has 24 units of KE which is then shared with C so they both have 22 units of KE.

Now suppose D collides with B. In free flight it loses 4 units of KE and gains 4 units of PE. When it collides with B it has 16 units of KE which is then shared with B so they both have 18 units of KE.

So we now have

At top: B (PE=14 + KE=18) D (PE=14 + KE=18)

At bottom: A (PE=10 + KE=22) C (PE=10 + KE=22)

So we have a temperature gradient because mean KE at top is now 18 and mean KE at bottom is now 22, a difference of 4.

Note also that now we have a state of maximum entropy and no unbalanced energy potentials. You can keep on imagining collisions, but they will all maintain KE=18 at top and KE=22 at bottom. Voila! We have thermodynamic equilibrium.

But, now suppose the top ones absorb new solar energy (at the top of the Venus atmosphere) and they now have KE=20. They are still cooler than the bottom ones, so what will happen now that the previous equilibrium has been disturbed?

Consider two more collisions like the first.

We start with

At top: B (PE=14 + KE=20) D (PE=14 + KE=20)

At bottom: A (PE=10 + KE=22) C (PE=10 + KE=22)

If B collides with A it has 24 units of KE just before the collision, but then after sharing they each have 23 units. Similarly, if C collides with D they each end up with 19 units of KE. So, now we have a new equilibrium:

At top: C (PE=14 + KE=19) D (PE=14 + KE=19)

At bottom: A (PE=10 + KE=23) B (PE=10 + KE=23)

Note that the original gradient (with a difference of 4 in KE) has been re-established as expected, and some thermal energy has transferred from a cooler region (KE=20) to a warmer region that was KE=22 and is now KE=23. The additional 2 units of KE added at the top are now shared as an extra 1 unit on each level, with no energy gain or loss.

That represents the process of downward diffusion of KE to warmer regions which I call "heat creep" as it is a slow process in which thermal energy "creeps" up the sloping thermal profile. It happens in all tropospheres, explaining how energy gets into the Venus surface, and explaining how the Earth's troposphere "supports" surface temperatures and slows cooling at night.

The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems always evolve toward thermodynamic equilibrium—the state with the maximum possible entropy.

An isothermal profile in a gravitational field is not isentropic, for the simple reason that, firstly you are assuming all molecules have the same kinetic energy, but secondly, we know the ones at the top have more gravitational potential energy.

So, consider the following thought experiment, starting with ...

Molecules at top: More PE + equal KE

Molecules at bottom: Less PE + equal KE

In such a situation you have an unbalanced energy potential because the molecules at the top have more energy than those at the bottom. Hence you do not have the state of maximum entropy, because work can be done.

Let's consider an extremely simple case of two molecules (A & B) in an upper layer and two (C & D) in a lower layer. We will assume KE = 20 initially and give PE values such that the difference in PE is 4 units ...

At top: A (PE=14 + KE=20) B (PE=14 + KE=20)

At bottom: C (PE=10 + KE=20) D (PE=10 + KE=20)

Now suppose A collides with C. In free flight it loses 4 units of PE and gains 4 units of KE. When it collides with C it has 24 units of KE which is then shared with C so they both have 22 units of KE.

Now suppose D collides with B. In free flight it loses 4 units of KE and gains 4 units of PE. When it collides with B it has 16 units of KE which is then shared with B so they both have 18 units of KE.

So we now have

At top: B (PE=14 + KE=18) D (PE=14 + KE=18)

At bottom: A (PE=10 + KE=22) C (PE=10 + KE=22)

So we have a temperature gradient because mean KE at top is now 18 and mean KE at bottom is now 22, a difference of 4.

Note also that now we have a state of maximum entropy and no unbalanced energy potentials. You can keep on imagining collisions, but they will all maintain KE=18 at top and KE=22 at bottom. Voila! We have thermodynamic equilibrium.

But, now suppose the top ones absorb new solar energy (at the top of the Venus atmosphere) and they now have KE=20. They are still cooler than the bottom ones, so what will happen now that the previous equilibrium has been disturbed?

Consider two more collisions like the first.

We start with

At top: B (PE=14 + KE=20) D (PE=14 + KE=20)

At bottom: A (PE=10 + KE=22) C (PE=10 + KE=22)

If B collides with A it has 24 units of KE just before the collision, but then after sharing they each have 23 units. Similarly, if C collides with D they each end up with 19 units of KE. So, now we have a new equilibrium:

At top: C (PE=14 + KE=19) D (PE=14 + KE=19)

At bottom: A (PE=10 + KE=23) B (PE=10 + KE=23)

Note that the original gradient (with a difference of 4 in KE) has been re-established as expected, and some thermal energy has transferred from a cooler region (KE=20) to a warmer region that was KE=22 and is now KE=23. The additional 2 units of KE added at the top are now shared as an extra 1 unit on each level, with no energy gain or loss.

That represents the process of downward diffusion of KE to warmer regions which I call "heat creep" as it is a slow process in which thermal energy "creeps" up the sloping thermal profile. It happens in all tropospheres, explaining how energy gets into the Venus surface, and explaining how the Earth's troposphere "supports" surface temperatures and slows cooling at night.

Yes, if surface temperature increases, evaporation and convection increase to cool and fully compensate. Also agreed that adiabatic compression fully explains the 'greenhouse effect', no need to come up with new concepts of "heat creep" etc.

No Stephen. Convection (which comprises diffusion and advection) is all about molecules colliding. Explain how new thermal energy absorbed high in the cold Venus troposphere from incident solar radiation at dawn then makes its way into the far hotter Venus surface and raises its temperature 5 degrees.

There never will be evidence of carbon dioxide or water vapour warming, because each cools. On Venus, carbon dioxide leads to considerably lower supported surface temperatures than would be the case with an atmosphere of less-radiating gases like hydrogen and helium.

Any skeptic who still thinks carbon dioxide is having any effect at all is a warmist in my view. There can be only one truth. Those denying the truth that these gases actually cool, as is blatantly obvious in temperature data (as far as water vapour is concerned) is a denier of the truth.

The truth that nearly all are denying, lukes or warmists, lies in a whole new paradigm based on the now-proven gravito-thermal effect.

This retired physics educator puts it succinctly in summarising it all after reading the text of my book

Essential reading for an understanding of the basic physical processes which control planetary temperatures. Doug Cotton shows how simple thermodynamic physics implies that the gravitational field of a planet will establish a thermal gradient in its atmosphere. The thermal gradient, a basic property of a planet, can be used to determine the temperatures of its atmosphere, surface and sub-surface regions. The interesting concept of “heat creep” applied to diagrams of the thermal gradient is used to explain the effect of solar radiation on the temperature of a planet. The thermal gradient shows that the observed temperatures of the Earth are determined by natural processes and not by back radiation warming from greenhouse gases. Evidence is presented to show that greenhouse gases cool the Earth and do not warm it.

Below is a comment I have just posted on Lucia's Blackboard in response to a common thought experiment attempting to disprove the existence of the gravito-thermal effect that is obvious in all planetary tropospheres.

The "argument has been put to me several times and is obviously yet another attempt among climatologists to rubbish what is of course a very threatening postulate, because it smashes the greenhouse.

The argument ... does not display a correct comprehension of Kinetic Theory, or indeed the manner in which molecules move and collide.

If a perfectly isentropic state were to evolve then all molecules in any given horizontal plane would have equal kinetic energy, and of course equal potential energy, just as after the first two collisions in the 4 molecule thought experiment above.

Now, the direction in which a molecule “takes off” in its next free path motion just after a collision is random – rather like what happens with snooker balls.

So two molecules with equal KE set out in different directions after the collision, but there is no requirement that they must have more KE to go upwards. They don’t travel far anyway. It’s not as if any one molecule goes up a matter of several cm before colliding with another, for example. In fact, they nearly all travel in a direction that is not straight up or down.

At thermodynamic equilibrium (as you can see in the 4 molecule experiment) when any molecule has an upward component in its direction, it loses KE that is exactly the amount of energy represented by the difference in gravitational potential energy between the height of the molecule it last collided with and that of the next molecule. With the thermal gradient in place, the next molecule it strikes will have KE that is less than the one it last struck, and its own KE will have been reduced to exactly the same KE that the next molecule already has.

So, at thermodynamic equilibrium all collisions involve molecules which had identical KE before the collision, and so they exit the collision process still having the same KE which is the mean KE for all molecules in the horizontal plane where the collision occurred.

Now, for a small height difference, H in a “closed system” where g is the acceleration due to gravity, the loss in PE for a small ensemble of mass M moving downwards will thus be the product M.g.H because a force Mg moves the gas a distance H. But there will be a corresponding gain in KE and that will be equal to the energy required to warm the gas by a small temperature difference, T. This energy can be calculated using the specific heat Cp and this calculation yields the product M.Cp.T. Bearing in mind that there was a PE loss and a KE gain, we thus have …

M.Cp.T = – M.g.H

T/H = -g/Cp

But T/H is the temperature gradient, which is thus the quotient -g/Cp. This is the so-called “dry adiabatic lapse rate” and we don’t need to bring pressure or density into the calculation.

Following on from my comment #126658 on Lucia's Blackboard, it appears that SkS team member Neal J. King made a huge error in assuming any molecules would run out of kinetic energy when they are moving upwards between collisions. In my four molecule thought experiment #126576 we are talking about a distance averaging the mean free path of air molecules between collisions. That's about 68 nanometres! Even in a whole kilometre air molecules only lose about 3% to 5% of their kinetic energy because that's how much the temperature drops.

So may I suggest that Neal J. King goes back to his Skeptical Science Team to work up a better "answer" to the trillion dollar question (which many will be asking when my book comes out) what's wrong with the Loschmidt gravito-thermal effect theory, which eliminates any need for explaining things with GH radiative forcing?

I would like to suggest another possibility for the lack of observed sensitivity of surface temperatures to GHG in the modern era which does not require overturning the entire foundation of radiative physics. I placed a series of posts in a thread at Tallbloke, particularly this one, and this one, which I think work out nicely.

"Illustration of an electrical circuit analogy to radiative-convective equilibrium in a planetary atmosphere. Pressure and heat capacity set the resistance [opacity] to infrared transmission illustrated as the resistor Rc above. GHGs set the resistance [opacity] to infrared transmission illustrated as the resistor Rt above. As noted, "Resistance Rc corresponds to convection "shorting out" the radiative resistance Rt, allowing more current [analogous to heat in the atmosphere] to escape. If the resistance [IR opacity] of Rt increases due to adding more greenhouse gases, the resistance [IR opacity] of Rc will automatically drop to re-establish balance and thus the current through the circuit remains the same, and analogously, the temperature of the surface of the planet remains the same and self-regulates."

I also agree with you that addition of CO2 will cool the planet by increasing radiative surface area and IR emissivity to space. That's probably why the stratosphere has cooled slightly over the satellite era. Why should CO2 have opposite effects in the stratosphere and troposphere? I would argue that it doesn't.

Further experimental proof of the Loschmidt gravito-thermal effect can be easily seen in a Ranque-Hilsch vortex tube wherein a force far greater than gravity separates a gas into measurably hotter and colder streams as it redistributes kinetic energy, just as happens in a planet's troposphere due to the force of gravity.

You cannot explain the gravitationally induced thermal gradient in a vortex tube.

You cannot explain how the extra energy gets into the Venus surface to raise its temperature with what has to be a net energy input. There cannot be a net energy input brought about by radiation from a colder atmosphere as that obviously would violate the Second Law.

The Venus atmosphere cannot magnify the incident solar radiation at TOA up to 14,000 to 16,000 watts per square metre that would be needed if radiation were adding energy to the surface to raise its temperature 5 degrees during the Venus day.

Oxygen and nitrogen molecules in Earth's troposphere absorb thermal energy by conduction and diffusion processes. They do most of the slowing of surface cooling because there are 2,500 times as many of them as there are carbon dioxide molecules..

I can explain why surface cooling slows right down and upward convection sometimes stops altogether in calm conditions in the early pre-dawn hours, even though the thermal gradient is still there.

I can explain why hydrostatic equilibrium is the same as thermodynamic equilibrium, because there can be only one state of maximum entropy.

Of the incident solar radiation entering Earth's atmosphere, NASA net energy diagrams showed 19% absorbed on the way in compared with only 15% absorbed on the way back up from the surface. What does that tell you about how the atmosphere gets warmed? It's like on Venus - more solar energy is absorbed on the way in.

I can explain why real world data (which I will publish in an Appendix to my book) proves with statistical significance that water vapour cools. The IPCC wants you to believe that it warms by a staggering amount of the order of 10 degrees per 1% of moisture in the atmosphere. That's simply not what it does, and only the most gullible of people would believe that to be the case.

I can explain why planets are neither warming or cooling significantly.

I can explain why the core of our Moon is kept hot by the Sun, as is the case for the cores of all planets and moons.

I can explain the temperatures in the Uranus troposphere where there is no surface and no significant source of insolation or internal energy.

I can explain all known and estimated temperature data above and below any surface on any planet or satellite moon.

The Ranque-Hilsch vortex tube provides evidence of the gravito-thermal effect. You would need to provide contrary empirical evidence.

You would also need to produce a valid explanation (not assuming the gravito-thermal effect) as to how the necessary thermal energy gets into the Venus surface in order to raise its temperature by 5 degrees during its sunlit hours.

BigWaveDave considers the gravito-thermal effect (seen in the vortex tube) worth your time thinking about …

“Because the import of the consequence of the radial temperature gradient created by pressurizing a spherical body of gas by gravity, from the inside only, is that it obviates the need for concern over GHG’s. And, because this is based on long established fundamental principles that were apparently forgotten or never learned by many PhD’s, it is not something that can be left as an acceptable disagreement.”